Question: The grades on a math midterm at Santa Rita are normally distributed with $\mu = 69$ and $\sigma = 3.5$. Umaima earned a $63$ on the exam. Find the z-score for Umaima's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Umaima's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{63 - {69}}{{3.5}}} $ ${ z \approx -1.71}$ The z-score is $-1.71$. In other words, Umaima's score was $1.71$ standard deviations below the mean.